They will store for several months in a cool dry shed or garage. The best way of using them is to chop them into slices, sprinkle with olive oil and roast in the oven. They are nice to accompany the Sunday roast, or you can include them in a pan of roast vegetables with other veggies like aubergines, red peppers, onion chunks, mushrooms and cherry tomatoes and serve with a lemon sauce (made up from lemon juice, a little chicken stock made from a chicken stock cube, thickened with cornflower.). You can also boil chunks until soft (about 10 mins) and cover them with a bolognaise sauce.
If you roast them, the skin will be hard so it's best to roast them with the skin on. The fruits will deteriorate in a warm kitchen once they've been cut so cut them into slices and store in a polythene bag in the fridge if you've got room, or cover the flesh tightly with clingfilm. I've been told you can also cut them into chunks and freeze them but I've never tried this.